Answer:
53 = 12t + 5
Explanation:
- We can model the situation using a linear equation, where cost (C) is a function of ticket quantity (t).
- Since tickets cost $12 each, 12 is the slope in our linear equation as cost increases by $12 per each ticket purchased.
- Furthermore, the $5 is our y-intercept as you'd pay $5 even if you didn't buy any tickets
Thus, our entire equation is C(t) = 12t + 5.
- Since you and your family pay a total of $53, we'd plug in 53 for c in our linear equation, which would allow us to solve for t, the number of tickets you and your family bought to end up with a total cost of $53.
Thus, our equation to determine how many tickets your family purchased is 53 = 12t + 5.
Optional Step: Check the validity of our answer:
To check that our equation would allow us accurately determine the number of tickets your family purchased to end up with a total cost of $53, we'd need to solve the equation for t and then plug in t:
(53 = 12t + 5) - 5
(48 = 12t) / 12
4 = t
53 = 12(4) + 5
53 = 48 + 5
53 = 53
Thus, our equation is correct.